What did Archbishop Chaput say? First, I think we need to go back to the beginning - to Christ.
We believe Jesus Christ elevated marriage to a Sacrament; he defended the origin of marriage, as a man cleaving to his wife, leaving his family to become one flesh with her. St. Paul said this Sacrament represents the great mystery of Christ and his Church. Theologians and saints through the ages have described marriage as an icon of the Holy Trinity; as the man and woman bond in great love, they bring forth another person, a child - likewise, the great love of Father and Son can only be manifested as another person, the Holy Ghost (an oversimplification, yes).
There are two sacraments in which the Church views them as "sacraments of service" - Holy Orders and Matrimony. The Catechism of the Catholic Church states: "The sacraments of Holy Orders and Matrimony are directed toward the salvation of others; if they contribute as well to personal salvation, it is through service to others that they do so. They confer a particular mission in Church and serve to build up the People of God." These sacraments of service have particular actions associated with them. For the priest, some of the actions are hearing confessions, offering Mass, and consecrating the bread and wine at the altar. For the married couple, some of the actions are having sex, raising a family, and passing on the faith to their children.
For the married couple, sex is a normal and healthy action of the married couple. One of the reasons why the Church has always taught that sex outside of marriage is fornication or adultery (depending on whom it's with) is because we have taken sex from its normal environment - the action of a loving, committed, married couple - and have divorced it from its place, putting it in another setting. If God intended "from the beginning" that man and woman be married (if called to that vocation), then we can assume that God intended "from the beginning" that sex was an activity reserved for marriage; obviously because the act of procreation is involved and God's first commandment to the new couple was, "Be fruitful and multiply, and fill the earth..."(Gen 1:28). God, through his revelation to the Jewish people and through the 2,000 year teachings of the Catholic Church, has consistently taught that sex is a gift of self between the married couple. God created it, Christ protected it, St. Paul showed us how we represent the marriage between Christ and Bride, the Church.
As each Christian denomination abandoned these timeless teachings, the Catholic Church is left standing alone. One by one, Christians started to embrace contraception, cohabitation, divorce, divorce and remarriage, pornography, and now homosexuality. But the teachings of the Church remain the same - sex is reserved for the married couple. It's like if I tried to consecrate the bread and wine during Mass - it's just not my role. I'm not able to do it, even if I think I should be allowed and even if I say the same words and perform the same actions.
And so, we're all called to chastity; if married, we remain loyal to our spouse and if single, we abstain from sexual relations with others. Straight and gay, married or single, we're all called to chastity.
But when we've committed mortal sin, we've offended God by our actions. Like it or not, God said fornication, adultery, sodomy, homosexuality - it's all mortal sin; we endanger our eternal life if we engage in these actions without repentance. That goes for me, too. We're all in the same boat. Now, this isn't a big deal - believe it or not, life is more than getting laid, although to hear the secular world talk, it's the only thing on their minds! My parents had a show on of a pregnant woman getting medical treatment for a gunshot wound and they were worried about the baby being harmed; thankfully, they found out with a sonogram that the baby was healthy. But they added, "He's really well-endowed!" Gee, thanks for that info. Even in the midst of trying to save two lives, there apparently is always time to admire someone's genitalia.
The point is that in our culture of hook ups, porn, contraception, and the acceptance of any consensual sexual relationship as legitimate, a call to chastity seems pretty counter-cultural - and insane. So, what Archbishop Chaput is saying (which is no different than what others, even Joseph Cardinal Ratzinger, has said) seems to be extreme and judgmental to many secular ears.
But if we take the Bible seriously, that fornication, adultery, and other sexual sins are sins that can lead to our eternal damnation, then what Archbishop Chaput is saying is just a defense of 2,000 years of Christian morality, which came from an even older Jewish tradition, all taught by God. For the Catholic, if we repent of our sin, that means we've rejected it and turned away from our sin and towards God; it means we, by God's grace, are trying to change. And if you turn to God with a contrite heart and a repentant spirit, confessing your sins to God, he absolves you from your sins - we hear this at every Confession. We are clean again, if we're sincere. And so, if sex outside of marriage (in the case of all people), sex with members of the same sex (homosexuals), and sex with a married person (those who are divorced and remarried) are mortal sins, it is very logical to say, "Undertaking to live as brother and sister is necessary for the divorced and civilly-remarried to receive reconciliation in the Sacrament of Penance, which could then open the way to the Eucharist. Such individuals are encouraged to approach the Sacrament of Penance regularly, having recourse to God’s great mercy in that sacrament if they fail in chastity."
It basically boils down to this, as Catholics. Christ told us what the Kingdom of Heaven was like, didn't he? He said, "The kingdom of heaven is like treasure hidden in a field, which a man found and covered up; then in his joy he goes and sells all that he has and buys that field. Again, the kingdom of heaven is like a merchant in search of fine pearls, who, on finding one pearl of great value, went and sold all that he had and bought it" (Mat 13:44-45). He is telling us that the Kingdom of Heaven is of great value. It is such a great value that a person should be willing to "sell all that he has" in order to obtain it. And yet, if we're told we need to give up sex in order to obtain the Kingdom of Heaven, do we hear the voice of Christ, echoing in the modern day, or do we grind our teeth and shake our fists and growl, "Who are YOU to tell me how to live my life?! How dare you judge me?!" To me, it's the voice of Christ, but in the modern era. It's Jesus speaking through Chaput, telling us how valuable the Kingdom of Heaven is and how much we should want to obtain it. I recommend reading the entire letter of the Archbishop instead of reacting to the spin of the secular media. I also recommend Benedict XVI's letter, which also encouraged this option of "living as brother and sister". Lastly, I recommend reading the Catechism's section on the Sixth Commandment, which covers chastity and human sexuality. All of this is focused on the human person and the dignity we should have before God and man; if we reduce ourselves to be mere sexual creatures out to fulfil our passions, then we've missed our mark and are not being treated as the dignified people God intends us to be. Find the great freedom and peace that exists through living a chaste life.